Clerics: Quite aside from being the "heals on wheels," clerics are the mystics, the touchstones with the divine, and quite often the moral compass of the party.

Thieves: I know that some grognards have expressed ambivalence about this class, suggesting that it takes away from the other classes, but it doesn't need to be so. Rather, the thief is the rogue who has no innate magical ability, who lives by his wits instead of a strong sword-arm, and has corresponding bonuses to his ability to perform stealthy actions.

Almost every other class in existence is simply one of these four with a few extra skills tacked on:

Assassins: Thieves who really like to backstab.

Barbarians, rangers: Fighting-men (or possibly thieves) with special skills for surviving in the wilderness.

Bards: Singing, spell-using thieves.

Paladins: Either fighting-men who "found religion," or weaker clerics that happen to be able to use swords.

Sorcerers: Magic-users for those who can't be bothered to pick their spells carefully and spend a few gold on making scrolls.

Don't get me started on prestige classes: A nifty idea that was poorly implemented and contributed greatly to the magical arms race that bugs me about later editions.

There are three classes from AD&D and after that actually do provide some variance, even if their broad niche is filled by one of the basic four: Druids, monks and illusionists. Druids and illusionists were no doubt wonderfully mysterious when first introduced, but the druid has been all-too-often played as a tree-hugger (elves suffer the same problem) while magic specialization has been made so weak that few players bother with it anymore. Hence, I'm leaving them out for now, with an option to introduce them (or similarly mysterious NPC classes) into the game later.

Monks pose a particular cultural problem in AD&D, since the game itself assumes a European medieval culture, and martial-art wielding monks are a distinctly oriental concept. Of course, in a fantasy world, there is no reason to assume that such martial arts could not arise in a predominantly European culture, but it still seems an oddity, perhaps because of a lack of other oriental-flavored classes. In my old 3.5 world, monks were the personal bodyguards and assassins of the Emperor of Callain, a distinctly Byzantine culture. I could conceivably introduce them similarly in Asryth, but I have another route in mind in a cleric variant which I will post later.

For the rest, I'm planning on introducing a reasonably loose set of "secondary skills" rules which would have beginning characters roll to see what their background was before they became adventurers as well as allow for characters to learn new skills as time went on--not automatically, but as a reward for successful adventuring (e.g., a fighting-man might spend a summer with a band of rangers he helped learning how to forage, track, and move stealthily through the woods). The point would not be to emulate 3e's strict points-per-level system, or to prevent characters without training from having a reasonable chance of success at whatever they might attempt, but to let characters get small bonuses to their rolls when attempting actions.